Bayesian-guided inverse design of hyperelastic microstructures: Application to stochastic metamaterials
This work addresses the challenge of efficient inverse design for stochastic metamaterials, which is incremental as it builds on existing Bayesian and active learning methods for optimization under constraints.
The paper tackles the problem of identifying a microstructure design that achieves a target macroscopic stress response from a large pool of candidates, where direct evaluation is infeasible due to high computational or experimental costs. The result is a Bayesian-guided inverse design framework that, in numerical tests with 50,000 candidates, requires labeling less than 0.5% of the dataset and achieves a prescribed error threshold with only a handful of oracle evaluations in most cases.
From a given pool of all feasible design variants, our aim is to identify a structure that achieves a target macroscopic stress response. For each candidate design, the response is obtained from a high-fidelity oracle, in particular, time- and resource-intensive computational homogenization or experiments. We consider the case where (i) the geometry cannot be conveniently parameterized, rendering gradient-based optimization inapplicable, and (ii) brute-force evaluation of all candidates is infeasible due to the cost of oracle queries. To tackle this challenge, we propose a Bayesian-guided inverse design framework that proceeds as follows. First, the dimensionality of the design variants is reduced through statistical feature engineering, and the resulting low-dimensional descriptors are mapped to effective constitutive parameters describing the macroscopic hyperelastic response. This mapping is modeled using a multi-output Gaussian process surrogate that accounts for correlations between the parameters. The surrogate is trained using uncertainty-driven active learning under severe budget constraints, allowing only a very limited number of high-fidelity oracle evaluations. Based on surrogate predictions, a finite number of promising candidates are shortlisted. Since the surrogate accuracy is inherently limited, the final selection of the optimal design is performed through high-fidelity oracle evaluations within the shortlist. In numerical test cases, we consider a dataset of 50,000 candidate structures. Active learning requires labeling less than half a percent of the full dataset. Bayesian-guided inverse design under unseen loading conditions reaches a prescribed error threshold with only a handful of oracle evaluations in the majority of cases.